APFIVE Electromagnetic Damping Time Constant
A circular loop of wire with radius $r$, mass $m$, and resistance $R$ moves with velocity $v$ perpendicular to a uniform magnetic field $B$. If the loop experiences a retarding force due to the induced current, what is the time constant $\tau$ of the loop’s exponential deceleration?
A
$$\tau = \dfrac{mR}{B \pi r^2}$$
B
$$\tau = \dfrac{B^2 \pi r^2 R}{m}$$
C
$$\tau = \dfrac{mR}{B^2 \pi^2 r^4}$$
D
$$\tau = \dfrac{m}{B^2 \pi r^2 R}$$
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